Theorem nn0expcld

Description: Closure of exponentiation of nonnegative integers. (Contributed by Mario Carneiro, 28-May-2016)

	Ref	Expression
Hypotheses	nn0expcld.1	|- ( ph -> A e. NN0 )
	nn0expcld.2	|- ( ph -> N e. NN0 )
Assertion	nn0expcld	|- ( ph -> ( A ^ N ) e. NN0 )

Proof

Step	Hyp	Ref	Expression
1		nn0expcld.1	|- ( ph -> A e. NN0 )
2		nn0expcld.2	|- ( ph -> N e. NN0 )
3		nn0expcl	|- ( ( A e. NN0 /\ N e. NN0 ) -> ( A ^ N ) e. NN0 )
4	1 2 3	syl2anc	|- ( ph -> ( A ^ N ) e. NN0 )